Question

In a circle with centre o an arc abc subtends an angle of 110 degree at the centre of the circle. The chord ab is produced to a point p. Then angle cbp is equal to

Answer 1

∠cbp  = 55°

Step-by-step explanation:

in a circle with centre o an arc abc subtends an angle of 110 degree at the centre of the circle

=>∠aoc  = 110°

Let say d is a point on other arc segment

then ∠adc = (1/2)∠aoc   ( angle subtended by chord ac at center and arc segment)

=> ∠adc = (1/2)110°

=> ∠adc = 55°

abcd is a cyclic Quadrilateral

Hence ∠abc + ∠adc = 180°

=>  ∠abc + 55°= 180°

=>∠abc  = 125°

∠abc  + ∠cbp  = 180°  ( straight line)

=>  125°    + ∠cbp  = 180°

=> ∠cbp  = 55°

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